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<p>Starting from involutive BE algebras, we redefine the quantum-MV algebras, by introducing and studying the notion of quantum-Wajsberg algebras. We define the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\vee \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>∨</mo> </math></EquationSource> </InlineEquation>-commutative quantum-Wajsberg algebras and we investigate their properties. We also prove that any Wajsberg algebra is a quantum-Wajsberg algebra, and give conditions for quantum-Wajsberg algebras to be Wajsberg algebras. Furthermore, we prove that Wajsberg algebras are both quantum-Wajsberg algebras and commutative quantum-B algebras. Finally, we provide certain conditions for quantum-MV algebras to be MV algebras.</p>

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Quantum-Wajsberg algebras

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Lavinia Corina Ciungu

摘要

Starting from involutive BE algebras, we redefine the quantum-MV algebras, by introducing and studying the notion of quantum-Wajsberg algebras. We define the \(\vee \) ∨ -commutative quantum-Wajsberg algebras and we investigate their properties. We also prove that any Wajsberg algebra is a quantum-Wajsberg algebra, and give conditions for quantum-Wajsberg algebras to be Wajsberg algebras. Furthermore, we prove that Wajsberg algebras are both quantum-Wajsberg algebras and commutative quantum-B algebras. Finally, we provide certain conditions for quantum-MV algebras to be MV algebras.